# Inertia

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Inertia is the resistance, of any physical object, to any change in its velocity. This includes changes to the object's speed, or direction of motion.

An aspect of this property is the tendency of objects to keep moving in a straight line at a constant speed, when no forces are upon them—and this aspect in particular is also called inertia.

The principle of inertia is one of the fundamental principles in classical physics that are still used today to describe the motion of objects and how they are affected by the applied forces on them.

Inertia comes from the Latin word, iners, meaning idle, sluggish. Inertia is one of the primary manifestations of mass, which is a quantitative property of physical systems. Isaac Newton defined inertia as his first law in his Philosophiæ Naturalis Principia Mathematica, which states: [1]

The vis insita, or innate force of matter, is a power of resisting by which every body, as much as in it lies, endeavours to preserve its present state, whether it be of rest or of moving uniformly forward in a straight line.

In common usage, the term "inertia" may refer to an object's "amount of resistance to change in velocity" (which is quantified by its mass), or sometimes to its momentum, depending on the context. The term "inertia" is more properly understood as shorthand for "the principle of inertia" as described by Newton in his First Law of Motion: an object not subject to any net external force moves at a constant velocity. Thus, an object will continue moving at its current velocity until some force causes its speed or direction to change.

On the surface of the Earth, inertia is often masked by the effects of friction and air resistance, both of which tend to decrease the speed of moving objects (commonly to the point of rest), and gravity. This misled the philosopher Aristotle to believe that objects would move only as long as force was applied to them:[2][3]

...it [body] stops when the force which is pushing the travelling object has no longer power to push it along...

## History and development of the concept

### Early understanding of motion

Prior to the Renaissance, the most generally accepted theory of motion in Western philosophy was based on Aristotle who around about 335 BC to 322 BC said that, in the absence of an external motive power, all objects (on Earth) would come to rest and that moving objects only continue to move so long as there is a power inducing them to do so. Aristotle explained the continued motion of projectiles, which are separated from their projector, by the action of the surrounding medium, which continues to move the projectile in some way.[4] Aristotle concluded that such violent motion in a void was impossible.[5]

Despite its general acceptance, Aristotle's concept of motion was disputed on several occasions by notable philosophers over nearly two millennia. For example, Lucretius (following, presumably, Epicurus) stated that the "default state" of matter was motion, not stasis.[6] In the 6th century, John Philoponus criticized the inconsistency between Aristotle's discussion of projectiles, where the medium keeps projectiles going, and his discussion of the void, where the medium would hinder a body's motion. Philoponus proposed that motion was not maintained by the action of a surrounding medium, but by some property imparted to the object when it was set in motion. Although this was not the modern concept of inertia, for there was still the need for a power to keep a body in motion, it proved a fundamental step in that direction.[7][8][9] This view was strongly opposed by Averroes and by many scholastic philosophers who supported Aristotle. However, this view did not go unchallenged in the Islamic world, where Philoponus did have several supporters who further developed his ideas.

### Theory of impetus

In the 14th century, Jean Buridan rejected the notion that a motion-generating property, which he named impetus, dissipated spontaneously. Buridan's position was that a moving object would be arrested by the resistance of the air and the weight of the body which would oppose its impetus.[10] Buridan also maintained that impetus increased with speed; thus, his initial idea of impetus was similar in many ways to the modern concept of momentum. Despite the obvious similarities to more modern ideas of inertia, Buridan saw his theory as only a modification to Aristotle's basic philosophy, maintaining many other peripatetic views, including the belief that there was still a fundamental difference between an object in motion and an object at rest. Buridan also believed that impetus could be not only linear, but also circular in nature, causing objects (such as celestial bodies) to move in a circle.

Buridan's thought was followed up by his pupil Albert of Saxony (1316–1390) and the Oxford Calculators, who performed various experiments that further undermined the classical, Aristotelian view. Their work in turn was elaborated by Nicole Oresme who pioneered the practice of demonstrating laws of motion in the form of graphs.

Shortly before Galileo's theory of inertia, Giambattista Benedetti modified the growing theory of impetus to involve linear motion alone:

"…[Any] portion of corporeal matter which moves by itself when an impetus has been impressed on it by any external motive force has a natural tendency to move on a rectilinear, not a curved, path."[11]

Benedetti cites the motion of a rock in a sling as an example of the inherent linear motion of objects, forced into circular motion.

### Classical inertia

Galileo Galilei

The principle of inertia which originated with Aristotle for "motions in a void" states that an object tends to resist a change in motion. According to Newton, an object will stay at rest or stay in motion (i.e. "maintain its velocity") unless acted on by a net external force, whether it results from gravity, friction, contact, or some other force. The Aristotelian division of motion into mundane and celestial became increasingly problematic in the face of the conclusions of Nicolaus Copernicus in the 16th century, who argued that the earth (and everything on it) was in fact never "at rest", but was actually in constant motion around the sun.[12] Galileo, in his further development of the Copernican model, recognized these problems with the then-accepted nature of motion and, at least partially as a result, included a restatement of Aristotle's description of motion in a void as a basic physical principle:

A body moving on a level surface will continue in the same direction at a constant speed unless disturbed.[13]

Galileo writes that "all external impediments removed, a heavy body on a spherical surface concentric with the earth will maintain itself in that state in which it has been; if placed in movement towards the west (for example), it will maintain itself in that movement."[14] This notion which is termed "circular inertia" or "horizontal circular inertia" by historians of science, is a precursor to, but distinct from, Newton's notion of rectilinear inertia.[15][16] For Galileo, a motion is "horizontal" if it does not carry the moving body towards or away from the centre of the earth, and for him, "a ship, for instance, having once received some impetus through the tranquil sea, would move continually around our globe without ever stopping."[17][18]

It is also worth noting that Galileo later (in 1632) concluded that based on this initial premise of inertia, it is impossible to tell the difference between a moving object and a stationary one without some outside reference to compare it against.[19] This observation ultimately came to be the basis for Einstein to develop the theory of Special Relativity.

The first physicist to completely break away from the Aristotelian model of motion was Isaac Beeckman in 1614.[20]

Concepts of inertia in Galileo's writings would later come to be refined, modified and codified by Isaac Newton as the first of his Laws of Motion (first published in Newton's work, Philosophiae Naturalis Principia Mathematica, in 1687):

Unless acted upon by a net unbalanced force, an object will maintain a constant velocity.

Note that "velocity" in this context is defined as a vector, thus Newton's "constant velocity" implies both constant speed and constant direction (and also includes the case of zero speed, or no motion). Since initial publication, Newton's Laws of Motion (and by inclusion, this first law) have come to form the basis for the branch of physics known as classical mechanics.[21]

The term "inertia" was first introduced by Johannes Kepler in his Epitome Astronomiae Copernicanae[22] (published in three parts from 1617–1621); however, the meaning of Kepler's term (which he derived from the Latin word for "idleness" or "laziness") was not quite the same as its modern interpretation. Kepler defined inertia only in terms of a resistance to movement, once again based on the presumption that rest was a natural state which did not need explanation. It was not until the later work of Galileo and Newton unified rest and motion in one principle that the term "inertia" could be applied to these concepts as it is today.[citation needed]

Nevertheless, despite defining the concept so elegantly in his laws of motion, even Newton did not actually use the term "inertia" to refer to his First Law. In fact, Newton originally viewed the phenomenon he described in his First Law of Motion as being caused by "innate forces" inherent in matter, which resisted any acceleration. Given this perspective, and borrowing from Kepler, Newton attributed the term "inertia" to mean "the innate force possessed by an object which resists changes in motion"; thus, Newton defined "inertia" to mean the cause of the phenomenon, rather than the phenomenon itself. However, Newton's original ideas of "innate resistive force" were ultimately problematic for a variety of reasons, and thus most physicists no longer think in these terms. As no alternate mechanism has been readily accepted, and it is now generally accepted that there may not be one which we can know, the term "inertia" has come to mean simply the phenomenon itself, rather than any inherent mechanism. Thus, ultimately, "inertia" in modern classical physics has come to be a name for the same phenomenon described by Newton's First Law of Motion, and the two concepts are now considered to be equivalent.

### Relativity

Albert Einstein's theory of special relativity, as proposed in his 1905 paper entitled "On the Electrodynamics of Moving Bodies" was built on the understanding of inertial reference frames developed by Galileo and Newton. While this revolutionary theory did significantly change the meaning of many Newtonian concepts such as mass, energy, and distance, Einstein's concept of inertia remained unchanged from Newton's original meaning. However, this resulted in a limitation inherent in special relativity: the principle of relativity could only apply to inertial reference frames. To address this limitation, Einstein developed his general theory of relativity ("The Foundation of the General Theory of Relativity," 1916), which provided a theory including noninertial (accelerated) reference frames.[23]

## Rotational inertia

Another form of inertia is rotational inertia (→ moment of inertia), the property that a rotating rigid body maintains its state of uniform rotational motion. Its angular momentum is unchanged, unless an external torque is applied; this is also called conservation of angular momentum. Rotational inertia depends on the object remaining structurally intact as a rigid body, and also has practical consequences. For example, a gyroscope uses the property that it resists any change in the axis of rotation.

## Notes

1. ^ Andrew Motte's English translation:Newton, Isaac (1846), Newton's Principia : the mathematical principles of natural philosophy, New York: Daniel Adee, p. 72
2. ^ Aristotle: Minor works (1936), Mechanical Problems (Mechanica), University of Chicago Library: Loeb Classical Library Cambridge (Mass.) and London, p. 407
3. ^ Pages 2 to 4, Section 1.1, "Skating", Chapter 1, "Things that Move", Louis Bloomfield, Professor of Physics at the University of Virginia, How Everything Works: Making Physics Out of the Ordinary, John Wiley & Sons (2007), hardcover, ISBN 978-0-471-74817-5
4. ^ Aristotle, Physics, 8.10, 267a1–21; Aristotle, Physics, trans. by R. P. Hardie and R. K. Gaye Archived 2007-01-29 at the Wayback Machine.
5. ^ Aristotle, Physics, 4.8, 214b29–215a24.
6. ^ Lucretius, On the Nature of Things (London: Penguin, 1988), pp. 60–65
7. ^ Sorabji, Richard (1988). Matter, space and motion : theories in antiquity and their sequel (1st ed.). Ithaca, N.Y.: Cornell University Press. pp. 227–228. ISBN 978-0801421945.
8. ^ "John Philoponus". Stanford Encyclopedia of Philosophy. 8 June 2007. Retrieved 26 July 2012.
9. ^ Darling, David (2006). Gravity's arc: the story of gravity, from Aristotle to Einstein and beyond. John Wiley and Sons. pp. 17, 50. ISBN 978-0-471-71989-2.
10. ^ Jean Buridan: Quaestiones on Aristotle's Physics (quoted at Impetus Theory)
11. ^ Giovanni Benedetti, selection from Speculationum, in Stillman Drake and I. E. Drabkin, Mechanics in Sixteenth Century Italy University of Wisconsin Press, 1969, p. 156.
12. ^ Nicholas Copernicus, The Revolutions of the Heavenly Spheres, 1543
13. ^ For a detailed analysis concerning this issue, see Alan Chalmers article "Galliean Relativity and Galileo's Relativity", in Correspondence, Invariance and Heuristics: Essays in Hounour of Heinz Post, eds. Steven French and Harmke Kamminga, Kluwer Academic Publishers, Dordrecht, 1991, ISBN 0792320859.
14. ^ Drake, S. Discoveries and Opinions of Galileo, Doubleday Anchor, New York, 1957, pp. 113–114
15. ^ See Alan Chalmers article "Galliean Relativity and Galileo's Relativity", in Correspondence, Invariance and Heuristics: Essays in Hounour of Heinz Post, eds. Steven French and Harmke Kamminga, Kluwer Academic Publishers, Dordrecht, 1991, pp. 199–200, ISBN 0792320859. Chalmers does not, however, believe that Galileo's physics had a general principle of inertia, circular or otherwise.
16. ^ Dijksterhuis E.J. The Mechanisation of the World Picture, Oxford University Press, Oxford, 1961, p. 352
17. ^ Galileo, Letters on Sunspots, 1613 quoted in Drake, S. Discoveries and Opinions of Galileo, Doubleday Anchor, New York, 1957, pp. 113–114.
18. ^ According to Newtonian mechanics, if a projectile on a smooth spherical planet is given an initial horizontal impetus, it will not remain on the surface of the earth. Various curves are possible depending on the initial speed and the height of launch. See Harris Benson University Physics, New York 1991, page 268. If constrained to remain on the surface, by being sandwiched, say, in between two concentric spheres, it will follow a great circle on the surface of the earth, i.e. will only maintain a westerly direction if fired along the equator. See "Using great circles" Using great circles
19. ^ Galileo, Dialogue Concerning the Two Chief World Systems, 1632 (full text).
20. ^ van Berkel, Klaas (2013), Isaac Beeckman on Matter and Motion: Mechanical Philosophy in the Making, Johns Hopkins University Press, pp. 105–110
21. ^ Dourmaskin, Peter (December 2013). "Classical Mechanics: MIT 8.01 Course Notes". MIT Physics 8.01. Retrieved September 9, 2016.
22. ^ Lawrence Nolan (ed.), The Cambridge Descartes Lexicon, Cambridge University Press, 2016, "Inertia."
23. ^ Alfred Engel English Translation:Einstein, Albert (1997), The Foundation of the General Theory of Relativity (PDF), New Jersey: Princeton University Press, p. 57, retrieved 30 May 2014

## References

• Ragep, F. Jamil (2001a). Tusi and Copernicus: The Earth's Motion in Context. Science in Context. 14. Cambridge University Press. pp. 145–163.
• Ragep, F. Jamil (2001b). "Freeing Astronomy from Philosophy: An Aspect of Islamic Influence on Science". Osiris, 2nd Series. 16 (Science in Theistic Contexts: Cognitive Dimensions): 49–64 & 66–71. Bibcode:2001Osir...16...49R. doi:10.1086/649338.
• Pfister, Herbert; King, Markus (2015). Inertia and Gravitation. The Fundamental Nature and Structure of Space-Time. The Lecture Notes in Physics. Volume 897. Heidelberg: Springer. doi:10.1007/978-3-319-15036-9. ISBN 978-3-319-15035-2.